The imaging capabilities of phased-array systems are governed by the properties of their array beamshape, directly linked to the instrument impulse response. To ensure good spatial resolution, beamshapes are designed with a very narrow main lobe, at the cost of a complex sidelobe structure, potentially leading to severe image artifacts. We propose the use of a new beamshape, called the Laplace beamshape, built with the Flexibeam framework. This beamshape trades spatial resolution for smoother sidelobes, resulting in an artifact-free image that is much easier to process. This tradeoff can be optimally assessed through a single parameter of the beamshape, allowing the analyst to perform a multi-scale analysis.